coefficient -- coefficient of a monomial

Usage:

coefficient(m,f)
Inputs:
- m, a ring element, a monomial
- f, a ring element, in the same ring R as m
Outputs:
- a ring element, the coefficient of the monomial m in f as an element of the coefficient ring of R

Description

i1 : R = GF(25,Variable=>a)[x,y,z];

i2 : f = ((a+1)*x+a*y+a^2*z)^2

                2                          2                               
o2 = (- 2a - 1)x  + (- a + 1)x*y + (a - 2)y  + 2x*z + (- 2a + 1)y*z + (2a +
     ------------------------------------------------------------------------
        2
     2)z

o2 : R

i3 : coefficient(y^2,f)

o3 = a - 2

o3 : GF 25

The returned value is an element of the coefficient ring, even in the case when that ring is another polynomial ring.

i4 : S = R[r,s,t];

i5 : coefficient(r,a*x*(r+a*s))

o5 = a*x

o5 : R

For the programmer

The object coefficient is a method function.

The source of this document is in Macaulay2Doc/functions/coefficient-doc.m2:35:0.

coefficient -- coefficient of a monomial

Description

See also

For the programmer